In general, horizontal-axis fluid-turbine rotor blades comprise two to five blades arranged evenly about a central axis and coupled to an electrical generation machine.
Generally speaking, a fluid turbine structure with an open unshrouded rotor design, captures energy from a fluid stream that is smaller in diameter than the turbine's rotor. In an open unshrouded fluid turbine, as fluid flows from the upstream side of the rotor to the downstream side, the average axial fluid velocity remains constant as the flow passes through the rotor plane. Energy is extracted at the rotor, resulting in a pressure drop on the downstream side of the rotor. The fluid directly downstream of the rotor consists of air that exists at sub-atmospheric pressure due to the energy extraction. The fluid directly upstream of the rotor consists of air that exists at greater-than-atmospheric pressure. The high-pressure upstream of the rotor deflects some of the upstream air around the rotor. In other words, a portion of the fluid stream is diverted around the open rotor as if by an impediment. As the fluid stream is diverted around the open rotor, it expands. This is referred to as flow expansion at the rotor. Because of the flow expansion, the upstream area of the columnar fluid stream, that may be captured by the open rotor turbine, is smaller than the area of the rotor.
The Betz limit calculates the maximum power that can be extracted by an open rotor turbine, from a volume of moving fluid. The Betz limit is derived from fluid dynamic control-volume theory for flow passing through an open rotor. According to the Betz limit, and independent of the design of the fluid turbine, a maximum of 16/27 of the total kinetic energy in a volume of moving fluid can be captured by an open-rotor turbine. Conventional turbines commonly produce 75% to 80% of the Betz limit, or about 44% of the total kinetic energy in a volume of moving fluid.
A fluid turbine power coefficient (Cp) is the power generated over the ideal power available by extracting all the wind kinetic energy approaching the rotor area. The Betz power coefficient of 16/27 is the maximum power generation possible based on the kinetic energy of the flow approaching a rotor swept area. For an open-rotor turbine, the rotor swept area used in the Betz Cp derivation is the system's maximum flow area described by the diameter of the rotor blades. The maximum power generation occurs when the rotor flow velocity is the average of the upstream and downstream velocity. This is the only rotor velocity that allows the flow-field to be reversible, and the power extraction to be maximized. At this operating point, the rotor velocity is 2/3 the wind velocity, the wake velocity is 1/3 the wind velocity, and the rotor flow has a non-dimensional pressure coefficient of −1/3 at the rotor exit. The −1/3 pressure coefficient is a result of the rotor wake flow expanding out to twice the rotor exit area downstream of the rotor station.
Induced drag is generated by a rotor blade due to the redirection of fluid during the generation of lift as a column of fluid flows through the rotor plane. The redirection of the fluid may include span-wise flow along the pressure side of the rotor blade along a radial direction toward the blade tip where the fluid then flows over to the opposite side of the blade. The fluid flow over the blade tips joins a chord-wise flow, otherwise referred to as bypass flow, forming rotor-tip vortices. The rotor-tip vortices mix with vortices shed from the trailing edge of the rotor blade to form rotor wake.
It is commonly known that rotor wake affects rotor intake. A column of fluid encounters a rotor as an impediment, in part, because a portion of the fluid flowing around the rotor expands in the wake of the rotor in a form referred to as the stream column. Fluid flowing around the rotor plane is referred to as the bypass flow. Bypass flow passes over the outer surface of the stream column. Increasing lift over the rotor, and hence increasing the amount of energy extracted from the stream column, creates slower-moving flow in the rotor wake, impeding flow through the rotor. This impediment increases the volume of the rotor wake. In other words, as more power is extracted at the rotor, the rotor stream column will expand and more fluid flow will bypass the rotor. If a significant amount of energy is extracted, most of the fluid flow will bypass the rotor and the rotor can effectively stop extracting energy. This is referred to as rotor stall. As a result, maximum power is achieved from the two opposing effects of increased power extraction resulting in relatively lower flow rates; and reduced power extraction resulting in relatively higher flow rates.
When a shrouded turbine is used for increased power extraction, in general, it extracts more power from the fluid stream than an open rotor by increasing the mass flow through the rotor plane, employing specially designed rotor blades to extract more power than their open-rotor turbine counterpart, and then by dissipating the wake to avoid diffuser stall. Diffuser stall occurs when the increased mass flow through the rotor encounters the ambient fluid stream down-stream of the rotor plane and causes a back-pressure at the rotor plane. Proposed solutions to diffuser stall include increasing the size of the wake area to allow for increased wake expansion and injecting high-energy fluid into the rotor wake. Both solutions have been proven to allow for rotor blade design that results in increased energy extraction at the rotor.
Turbines in the power production range of 1 kW or less often have tail fins for yawing the turbine into the wind. A tail fin causes turbulence in the wake back pressure in the rotor plane, thus causing a reduction in mass flow through the rotor and hence a reduction in power production.
Aside from the aerodynamic challenge of eliminating the causes of diffuser stall, shrouded turbines are heavier than their open rotor counterparts; they are more expensive to produce and construct; and they create a bluff body when hit by commonly occurring side winds and gusts. Side winds produce a large amount of drag force that places considerable strain on structural components.
Wind shear is the difference in wind speed by height. The higher the wind shear, the higher the wind velocity at the upper region of a rotor plane compared with the wind velocity at the lower regions of the rotor plane. As turbines increase in scale, they take advantage of higher wind velocities at higher altitudes while also experiencing greater wind shear. Extreme wind shear is responsible for noise emissions that do not meet noise-pollution regulations.
Stress and strain on rotor blades is a considerable concern in the wind turbine industry. A rotor blade rotating in a high wind-shear environment will experience variation in wind velocities and therefore more down-wind flexing while passing through the upper regions of the rotor plane than while passing through the lower regions of the rotor plane. Wind-shear increases as turbines increase in size.
Noise caused by wind turbines is a product of wind velocity and rotor blade trailing-edge vortices and tip vortices. Trailing-edge and tip vortices create white-noise.
Tower signature is a term often used to describe the sound created when rotor tip vortices encounter the turbine tower. The tower interrupts the flow of the trailing-edge and tip vortices, occurring as each blade passes the tower. This sound pattern interrupts the white noise, causing a low-frequency tonal signal of sharply rising and falling pulses. Complaints of turbine noise are in regard to the pattern of the tonal signal more than the white noise generated by wind turbines. Some studies have shown that this tonal signal also occurs in the infrasound range, typically about 0.75 Hz, 1.5 Hz, 2.25 Hz, 3.0 Hz, and so on. At this frequency these pulses may be felt or sensed more than heard by the ears.
Tip-speed ratio (λ) is the ratio between the tangential speed of the rotor blade tip and the actual wind velocity. This is expressed by the following formula:
  λ  =                    Rotor        ⁢                                  ⁢        tip            -      speed              Wind      ⁢                          ⁢      velocity      
The tip-speed can also be calculated as follows:
  λ  =            ω      ⁢                          ⁢      R        v  
Where ω is the rotor rotational speed in radians/second, R is the rotor radius in meters and v is the wind velocity.
The tip-speed ratio is an indicator of the efficiency of the turbine. The power coefficient (Cp) is a quantity that expresses the fraction of power in the wind that is being extracted by the turbine.
  Cp  =            P      E              P      W      
Where PE is the total energy extracted by a rotor and PW is the total power in a column of wind, of a diameter equal to the rotor diameter.
A fluid-power coefficient (Cp) is a function of the power generated by the turbine and the total power available in the column of fluid, the diameter of the rotor plane and the velocity of the fluid. The efficiency of a mechanical generator is less than 100%; therefore, measurements studied are appropriate relative measurements and do not predict the absolute power coefficient of any of the rotors tested and mentioned herein.
The yaw axis of a delta wing is stabilized through the backward sweep of the wings. The swept planform, when yawed out of the relative wind, creates more lift on the advancing wing and also more drag, and thus the advancing wing slows until equilibrium between the two wings is achieved. In other words, if one wing advances ahead of the other, it presents more area to the wind and causes more drag on that side. This causes the advancing wing to go slower, relative to the wind, and to fall back. The wing is at equilibrium when the aircraft is traveling straight into the relative wind, and both wings present the same amount of area to the wind.
The term ‘small wind turbine’ refers to wind turbines that produce energy in the range of 1 kilowatt or less. Small wind turbines are commonly self-yawing. Small wind turbines do not need motors to yaw the turbine into the wind.
A need exits for a fluid turbine rotor blade that provides increased rotor tip speed, reduced noise due to tip and trailing-edge vortices and tower signature, and reduced blade loading.